Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation . If a tuning fork for the note above middle on an even-tempered scale ( , the tone by which an orchestra tunes itself) has a frequency of 440 hertz (cycles per second), find . If the maximum displacement of the end of the tuning fork is millimeter, determine the equation that describes the movement of the tuning fork.
Source: David Lapp. Physics of Music and Musical Instruments. Medford, M A:Tufts University, 2003
. If the maximum displacement of the end of the tuning fork is millimeter,determine the equation that describes the movement of the tuning fork.
Answer to Problem 53AYU
Explanation of Solution
Given:
The end of a tuning fork moves in simple harmonic motion described by the equation
If a tuning fork for the note above middle on an even–tempered scale (, the tone by which an orchestra 4tunes itself) has a frequency of 440 hertz (cycles per second).find . If the maximum displacement of the end of the tuning fork is millimeter,
Formula used:
Calculation:
The maximum displacement is the amplitude. Therefore .
The frequency is given by
Therefore and the movement of the tuning fork is described by the equation
substituting the values we get,
Chapter 8 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
College Algebra with Modeling & Visualization (5th Edition)
Pre-Algebra Student Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning